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<h2><span class="refentrytitle">Function template integrate</span></h2>
<p>boost::numeric::odeint::integrate — Integrates the ODE without observer calls. </p>
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<h2 xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" class="refsynopsisdiv-title">Synopsis</h2>
<div xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" class="refsynopsisdiv"><pre class="synopsis"><span class="comment">// In header: &lt;<a class="link" href="../../../header/boost/numeric/odeint/integrate/integrate_hpp.html" title="Header &lt;boost/numeric/odeint/integrate/integrate.hpp&gt;">boost/numeric/odeint/integrate/integrate.hpp</a>&gt;

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<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> System<span class="special">,</span> <span class="keyword">typename</span> State<span class="special">,</span> <span class="keyword">typename</span> Time<span class="special">&gt;</span> 
  <span class="identifier">size_t</span> <span class="identifier">integrate</span><span class="special">(</span><span class="identifier">System</span> system<span class="special">,</span> <span class="identifier">State</span> <span class="special">&amp;</span> start_state<span class="special">,</span> <span class="identifier">Time</span> start_time<span class="special">,</span> 
                   <span class="identifier">Time</span> end_time<span class="special">,</span> <span class="identifier">Time</span> dt<span class="special">)</span><span class="special">;</span></pre></div>
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<a name="idm23941"></a><h2>Description</h2>
<p>Integrates the ODE given by system from start_time to end_time starting with start_state as initial condition and dt as initial time step. This function uses a dense output dopri5 stepper and performs an adaptive integration with step size control, thus dt changes during the integration. This method uses standard error bounds of 1E-6. No observer is called.</p>
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<th align="left">Note</th>
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<tr><td align="left" valign="top"><p>A second version of this function template exists which explicitly expects the value type as template parameter, i.e. integrate&lt; double &gt;( sys , x , t0 , t1 , dt );</p></td></tr>
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<td><p><span class="term">Parameters:</span></p></td>
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<td><p><span class="term"><code class="computeroutput">dt</code></span></p></td>
<td><p>Initial step size, will be adjusted during the integration. </p></td>
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<td><p><span class="term"><code class="computeroutput">end_time</code></span></p></td>
<td><p>End time of the integration. </p></td>
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<td><p><span class="term"><code class="computeroutput">start_state</code></span></p></td>
<td><p>The initial state. </p></td>
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<td><p><span class="term"><code class="computeroutput">start_time</code></span></p></td>
<td><p>Start time of the integration. </p></td>
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<td><p><span class="term"><code class="computeroutput">system</code></span></p></td>
<td><p>The system function to solve, hence the r.h.s. of the ordinary differential equation. </p></td>
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<td><p><span class="term">Returns:</span></p></td>
<td><p>The number of steps performed. </p></td>
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<td align="right"><div class="copyright-footer">Copyright © 2009-2015 Karsten Ahnert and Mario Mulansky<p>
        Distributed under the Boost Software License, Version 1.0. (See accompanying
        file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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